1. Tardigrade
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  4. Two rigid bodies A and B rotate with rotational kinetic energies EA and EB respectively. The moments of inertia of A and B about the axis of rotation are IA and IB respectively. If IA=(IB/4) and EA=100 EB the ratio of angular momentum (LA) of A to the angular momentum (LB) of B is:

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Q. Two rigid bodies A and B rotate with rotational kinetic energies $ {{E}_{A}} $ and $ {{E}_{B}} $ respectively. The moments of inertia of A and B about the axis of rotation are $ {{I}_{A}} $ and $ {{I}_{B}} $ respectively. If $ {{I}_{A}}=\frac{{{I}_{B}}}{4} $ and $ {{E}_{A}}=100\,{{E}_{B}} $ the ratio of angular momentum $ ({{L}_{A}}) $ of A to the angular momentum $ ({{L}_{B}}) $ of B is:

JIPMERJIPMER 2001

Solution:

From the formula, rotational K.E. $ {{E}_{rotational}}=\frac{1}{2}I{{\omega }^{2}}=\frac{{{L}^{2}}}{2I} $ $ (\because L=I\omega ) $ Therefore, $ {{L}^{2}}=2EI $ Hence $ L_{A}^{2}=2{{E}_{A}}{{I}_{A}} $ ?(i) and $ L_{B}^{2}=2{{E}_{B}}{{I}_{B}} $ ?(ii) From equation (i) and (ii) $ \frac{{{L}_{A}}}{{{L}_{B}}}=\sqrt{\frac{2{{E}_{A}}{{I}_{B}}}{2{{E}_{B}}{{I}_{A}}}}=\sqrt{\frac{100}{4}}=5 $ $ \left( \begin{align} & \because \,\,\,\,\,\,\,\,\frac{{{E}_{B}}}{{{E}_{A}}}=4 \\ & \text{and}\,\,\,\frac{{{I}_{A}}}{{{I}_{B}}}=100 \\ \end{align} \right) $